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What seemed to trigger the fight between Gene and Quakenbush in the Naguamsett?
"Maimed."
The fact that Quakenbush called Gene "maimed" triggered something inside of Gene that related to Finny, causing Gene to lash out. Only later did he realize this too, that Gene wasn't the one maimed, Finny was.
"Who the hell are you anyway."
It could also have been the fact that Gene wasn't as 'high class' as the other boys at the school, and everyone knew it. He was there because he made it, not because money let him there, and he was getting to a breaking point from being beaten and beaten. Maybe this was the final straw.